mirror of https://github.com/zcash/pasta.git
33 lines
882 B
Python
Executable File
33 lines
882 B
Python
Executable File
#!/usr/bin/python3
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# This checks the cases k = 1 and k = 2 needed to complete the proof of the
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# injectivity lemma in Appendix C of <https://eprint.iacr.org/2019/1021>.
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from itertools import product
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from collections import namedtuple
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cd_pair = namedtuple('cd_pair', ['c', 'd'])
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def c_d():
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yield cd_pair(-1, 0)
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yield cd_pair( 1, 0)
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yield cd_pair( 0, -1)
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yield cd_pair( 0, 1)
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def sums_mod4(cd):
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return ((2**(k+1) + sum([cd[j].c * (2**j) for j in range(k)])) % 4,
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(2**(k+1) + sum([cd[j].d * (2**j) for j in range(k)])) % 4)
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for k in (1, 2):
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M_k = [list(s) for s in product(c_d(), repeat=k)]
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assert(len(M_k) == 4**k)
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for cd in M_k:
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print("%r -> %r" % (cd, sums_mod4(cd)))
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for (cd, cd_dash) in product(M_k, repeat=2):
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if cd[0] != cd_dash[0]:
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assert(sums_mod4(cd) != sums_mod4(cd_dash))
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print("QED")
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